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Cusps and Corners in One-Dimensional Quantum Mechanics

Dr. Donald Franceschetti

Physics Department, The University of Memphis

October 1, 2008, 4:00pm, Manning Hall 201

Refreshments served at 3:30pm, Manning Hall 222

One-dimensional problems are often used to teach the basics of quantum mechanics.  The problems considered often involve wave functions with a cusp or corner, that is, a point where the wave function is continuous but its first derivative is not. 

I will show that it is nonetheless possible to express the second derivative and thus the kinetic energy of the particle described by the wave equation even at the singular point. 

This approach is used to explore the energetics of particles moving in a potential with multiple delta function wells.  Implications for modeling the chemical bond will be discussed.

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